Question

which type of collision would have the least amount of total energy right before the collision happens?
o a player #84 running and hitting the soccer ball.
o b player #84 running and hitting another player who is also running.
o c player #84 running and hitting the ground.

Explanation:

Step1: Analyze the mass of objects involved

The total energy before collision is related to the kinetic energy formula \(K = \frac{1}{2}mv^{2}\). Assume the speed \(v\) of the player (\(m_{player}\)) is similar in all cases.

• For option a: The mass involved is \(m_{player}+m_{soccer - ball}\). A soccer - ball has a relatively small mass (\(m_{soccer - ball}\approx0.45\space kg\)).
• For option b: The mass involved is \(m_{player}+m_{other - player}\). Assuming two players have similar masses (\(m_{player}\approx70 - 80\space kg\)), the total mass \(m = m_{player1}+m_{player2}\) is large.
• For option c: The mass involved is \(m_{player}+m_{ground}\). But when the player hits the ground, the part of the ground that is effectively in collision (the part that deforms or moves due to the collision) has a very large mass compared to the soccer - ball. However, if we consider the kinetic energy of the moving objects (the player is moving, and the soccer - ball in option a is also moving, while the ground in option c is (effectively) at rest. The kinetic energy of the system before collision is mainly from the moving objects. The soccer - ball has a much smaller mass than another player.

Answer:

A. Player #84 running and hitting the soccer ball.